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tijdreeks bevolkingstotaal

*The author of this computation has been verified*

R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Sun, 26 Dec 2010 10:36:08 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/26/t1293359627da6wx3yrv4lpp0d.htm/, Retrieved Sun, 26 Dec 2010 11:33:50 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/26/t1293359627da6wx3yrv4lpp0d.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

5140 4749 3635 4305 5805 4260 3869 7325 9280 6222 3272 7598 1345 1900 1480 1472 3823 4454 3357 5393 8329 4152 4042 7747 1451 911 -406 1387 2150 1577 2642 4273 8064 3243 1112 2280 505 744 -1369 -531 1041 2076 577 5080 6584 3761 294 5020 1141 3805 2127 2531 3682 3263 2798 5936 10568 5296 1870 4390 3707 5201 3748 5282 5349 6249 5517 8640 15767 8850 5582 6496 3255 6189 6452 5099 6833 7046 7739 10142 16054 7721 6182 6490 3704 6235 4655 5072 3640 5147 5703 11889 15603 9589

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.502778	-4.525	1e-05
2	0.194575	1.7512	0.041851
3	-0.238493	-2.1464	0.017415
4	0.153395	1.3806	0.085607
5	-0.056918	-0.5123	0.304931
6	0.054954	0.4946	0.311115
7	-0.013535	-0.1218	0.451674
8	-0.119972	-1.0798	0.141729
9	0.192983	1.7368	0.043108
10	-0.156812	-1.4113	0.080992
11	0.211616	1.9045	0.030195
12	-0.400193	-3.6017	0.000272
13	0.276629	2.4897	0.007417
14	-0.029975	-0.2698	0.394009
15	-0.019003	-0.171	0.432313
16	-0.037766	-0.3399	0.367407
17	0.051568	0.4641	0.321907
18	-0.052282	-0.4705	0.319618
19	0.031621	0.2846	0.388343
20	0.094239	0.8481	0.199427
21	-0.159511	-1.4356	0.077484
22	-0.035519	-0.3197	0.375019
23	0.033681	0.3031	0.381285
24	0.065464	0.5892	0.278691
25	-0.043913	-0.3952	0.346861
26	-0.059583	-0.5362	0.296628
27	0.133761	1.2039	0.116077
28	-0.103918	-0.9353	0.176217
29	0.101611	0.9145	0.181584
30	-0.080023	-0.7202	0.236736
31	0.117828	1.0604	0.146046
32	-0.179962	-1.6197	0.054596
33	0.204947	1.8445	0.034381
34	-0.149679	-1.3471	0.09085
35	0.058874	0.5299	0.298828
36	-0.095438	-0.8589	0.196453
37	0.077448	0.697	0.24389
38	0.060399	0.5436	0.294107
39	-0.141131	-1.2702	0.103828
40	0.053028	0.4773	0.317234
41	-0.048096	-0.4329	0.333133
42	0.057876	0.5209	0.301934
43	-0.078676	-0.7081	0.240462
44	0.146978	1.3228	0.094812
45	-0.232198	-2.0898	0.019887
46	0.274801	2.4732	0.007741
47	-0.110788	-0.9971	0.160844
48	0.077114	0.694	0.244826

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.502778	-4.525	1e-05
2	-0.077905	-0.7011	0.242612
3	-0.23188	-2.0869	0.02002
4	-0.081308	-0.7318	0.233211
5	-0.010777	-0.097	0.461487
6	0.001533	0.0138	0.494514
7	0.043525	0.3917	0.348147
8	-0.148029	-1.3323	0.093256
9	0.102866	0.9258	0.178651
10	-0.022149	-0.1993	0.421246
11	0.130372	1.1733	0.122048
12	-0.282704	-2.5443	0.006424
13	-0.09387	-0.8448	0.200346
14	0.163882	1.4749	0.072053
15	-0.120897	-1.0881	0.139896
16	-0.062439	-0.5619	0.287851
17	0.080128	0.7212	0.236446
18	-0.045231	-0.4071	0.342512
19	-0.00238	-0.0214	0.491482
20	0.072613	0.6535	0.257637
21	0.003764	0.0339	0.486528
22	-0.256408	-2.3077	0.011785
23	-0.058964	-0.5307	0.298547
24	-0.051744	-0.4657	0.321342
25	-0.062111	-0.559	0.288852
26	-0.063504	-0.5715	0.284609
27	0.080215	0.7219	0.236206
28	-0.01783	-0.1605	0.436454
29	0.084509	0.7606	0.224557
30	-0.011407	-0.1027	0.459241
31	0.149933	1.3494	0.090485
32	-0.025743	-0.2317	0.408684
33	0.019403	0.1746	0.430904
34	-0.166755	-1.5008	0.068649
35	0.017181	0.1546	0.43875
36	-0.121071	-1.0896	0.139553
37	-0.123105	-1.1079	0.135583
38	0.119936	1.0794	0.141802
39	-0.002483	-0.0223	0.491114
40	-0.212045	-1.9084	0.029941
41	0.094454	0.8501	0.198891
42	-0.002527	-0.0227	0.490955
43	-0.120868	-1.0878	0.139951
44	-0.075417	-0.6787	0.249616
45	-0.08458	-0.7612	0.224368
46	0.097122	0.8741	0.192325
47	0.059461	0.5351	0.297007
48	0.044361	0.3992	0.345382

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293359627da6wx3yrv4lpp0d/16jaw1293359765.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293359627da6wx3yrv4lpp0d/16jaw1293359765.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293359627da6wx3yrv4lpp0d/2zarh1293359765.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293359627da6wx3yrv4lpp0d/2zarh1293359765.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293359627da6wx3yrv4lpp0d/3zarh1293359765.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293359627da6wx3yrv4lpp0d/3zarh1293359765.ps (open in new window)

Parameters (Session):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

R code (references can be found in the software module):

if (par1 == 'Default') {

par1 = 10*log10(length(x))

} else {

par1 <- as.numeric(par1)

}

par2 <- as.numeric(par2)

par3 <- as.numeric(par3)

par4 <- as.numeric(par4)

par5 <- as.numeric(par5)

if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'

par7 <- as.numeric(par7)

if (par8 != '') par8 <- as.numeric(par8)

ox <- x

if (par8 == '') {

if (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

} else {

x <- log(x,base=par8)

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='picts.png')

op <- par(mfrow=c(2,1))

plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')

if (par8=='') {

mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

} else {

mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')

mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')

}

plot(x,type='l', main=mytitle,xlab='time',ylab='value')

par(op)

dev.off()

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)

dev.off()

(myacf <- c(racf$acf))

(mypacf <- c(rpacf$acf))

lengthx <- length(x)

sqrtn <- sqrt(lengthx)

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

a<-table.element(a,'P-value',header=TRUE)

a<-table.row.end(a)

for (i in 2:(par1+1)) {

a<-table.row.start(a)

a<-table.element(a,i-1,header=TRUE)

a<-table.element(a,round(myacf[i],6))

mytstat <- myacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Time lag k',header=TRUE)

a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)

a<-table.element(a,'T-STAT',header=TRUE)

a<-table.element(a,'P-value',header=TRUE)

a<-table.row.end(a)

for (i in 1:par1) {

a<-table.row.start(a)

a<-table.element(a,i,header=TRUE)

a<-table.element(a,round(mypacf[i],6))

mytstat <- mypacf[i]*sqrtn

a<-table.element(a,round(mytstat,4))

a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable1.tab')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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